The prefixes mis- and mal- basically mean the same thing. Mal-, from French, meaning "bad, badly, ill" and mis-, from Old English, meaning "bad, wrong". In some cases, mis- can derive from mes- (French) meaning bad(ly), wrong(ly).
From what I've noticed, the mis- prefix can be attached to any word of any origin but mal- seems to be reserved for words of French origin. For example: misaligned is a combination of mis and aligned (Old English + Middle French) and misidentify is a combination of mis and identify (Old English + French).
However, all the examples I checked with a mal- prefix are pure French, for example: malfeasance, malformed and malfunction.
So the question: Is it true that mal- can only be attached to words opf French origin? If so, is that because the words entered the English language with the prefix already attached?